Oh, what a happy little sequence we have here! To find the pattern, we can see that each term is generated by multiplying the previous term by 2 and then adding 2. So, the nth term can be found using the formula 2^n * 2 - 2. Isn't that just a delightful little formula?
Chat with our AI personalities
To find the nth term of a sequence, we first need to identify the pattern or rule that governs the sequence. In this case, we can see that each term is obtained by multiplying the previous term by 3 and then adding 2. So, the nth term can be expressed as: (a_n = 4 \times 3^{n-1} + 2), where n represents the position of the term in the sequence.
Oh, dude, chill out! The nth term of that sequence is 3n^2 + 1. So, like, if you plug in n=1, you get 4, n=2 gives you 10, n=3 gives you 28, and n=4 gives you 82. It's like a math magic trick, but with numbers.
To find the nth term in a quadratic sequence, we first need to determine the pattern. In this case, the difference between consecutive terms is increasing by 3, 5, 7, 9, and so on. This indicates a quadratic sequence. To find the 9th term, we need to use the formula for the nth term of a quadratic sequence, which is given by: Tn = an^2 + bn + c. By plugging in n=9 and solving for the 9th term, we can find that the 9th term in this quadratic sequence is 74.
t(n) = 3(n-1) + 1, for n = 1, 2, 3, etc
82 + 82 = 164
The square root of 82 is about 9.06
41 mins